Is the video game okami related to the legend

Yes it is. Most of the characters and bosses are taken from Japanese folklore, with a few differences. For example, according to folklore Orochi was defeated by the storm god Sussano.
Issun 'One Inch Boy' is a character from Japanese legend.

All of the weapons are based on items from Japanese folklore and the three weapon classes are based on the crown jewels of the Japanese Royal Family.
The name of the country Okami is set in is called 'Nippon' which is the Japanese name for Japan. The English word 'Japan' is a corrupted form of the Chinese for Japan.

--SPOILERS--
Traditional Japanese belief states that the King of the Sea is a dragon who lives in the Dragon palace, which is made of red coral.
In Japanese folk-tales foxes are portrayed as cunning, magical animals able to take human form.